Well, in order for it to be a ring, it would have to be an abelian group under addition right? In particular, it would have to contain the additive identity, but what is the additive identity? What is its determinant?
I have been asked to show that the set of n x n real matrices with determinant 1 is not a ring.
I've been fine with this topic so far, but this question stumped me. I'm not sure how I can go about manipulating examples of n x n matrices with the only piece of information that I have being that det(M) = 1. The only thing I can think of is linking it in some way with invertible matrices.